We know from classical demonstrations such as simultaneous contrast that the lightness of an image region can be strongly influenced by its local border contrast. More generally, though, lightness depends on a combination of the local border contrast with the contrasts of other borders within the region's extended surround. In previous work, my colleagues and I introduced a quantitative model of lightness computation based on the idea that lightness is computed from weighted sum across space of logarithms of luminance ratios at edges (edge integration). This model accounts with great quantitative precision for lightness judgments in simple stimuli such as disks surrounded by rings (Rudd & Zemach, 2004, 2005). Here I apply the most recent version of this model (Rudd & Popa, 2007)—which combines edge integration with a contrast gain control mechanism acting between borders—to the problem of predicting the lightness of the steps in a staircase Gelb display. Experiments by Gilchrist and his colleagues have revealed two interesting quantitative properties of lightness perception in the staircase Gelb display. First, the range of perceived reflectances of the staircase steps is strongly compressed relative to the actual physical reflectance range. Second, when the staircase is surrounded by a white frame the perceived reflectance range becomes much more veridical (less compressed), an effect known as “insulation” (Gilchrist et al., 1999). I will explain how the edge integration model accounts for both the compression and insulation effects. The results are consistent with a general neural scheme for computing lightness involving a weighted combination of edge-based filling-in signals whose gains are modulated by the surrounding spatial context.